Equivalences for weak crossed products

In this article, we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two weak crossed biproducts. As an application, we show that the main results proved by Panaite in [12] (see also [11]), for Brzezinski's crossed products, admits a substantial reduction in the imposed conditions.